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From these illustrations we derive the following
A. Bring the given denominations to the lowest denomination mentioned, for a numerator.
Q. How do you obtain the denominator ?
A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator.
More Exercises for the Slate. 2. What part of 1 £. is 2 s. 6 d.
A. = 3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz. ?
A. 398 4. What part of 1 vard is 3 qrs. 3 na. ?. A. tá 5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt. ?**
A. 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. 1 gill?
A. gota 7. What part of 15 pipes is 25 galls. ?
A. g. 8. What part of 2 miles is 7 fur. 11 in. 2 b. c. ?
A. 78332 9. What part of 1 month is 19 days ?
A. 38. 10. What part of 1 month is 25 days, 13 hours ?
A. 918 11. What part of 1 month is 22 days, 15 h. 1 min.?"
9 XLIX. TO REDUCE A FRACTION TO WHOLE Num
BERS OF LESS DENOMINATIONS, OR, TO FIND THE VALUE OF A FRACTION. 1. How much is of a shilling? How much It of a lb.'
of a lb.? Hoe of a lb. ? it of a lb.? 14 of a Ib.; end of 1 qr. of a cwt. ? ? g? 18? 37? 1 an hour! ? *?
Operation by Slate illustrated. 1 What is the value of of a pound ?
Q. How do you proNumer. 5
ceed in this example?
and why? 20 s.
A. Aš 1 £. = 205, Denom. 6)100(16 s. of one pound is iše
same as of 20 s., 711], to get of 20, we in iltiply the numerator 5 and 20 together, mak
ing 100; which, divid 16 s. 8 d. Ans. 4
ed by the denominator 12
6, gives 16 s. and of
another shilling re48 (8 d.
maining. This = 48
of 12 d.; then, of
12 d.=8 d.
A. By as many of the next denomination as make one of that; that is, pounds by what makes a pound, ounces by what makes an ounce, as in Reduction of whole numbers.
Q. What do you divide the product by ?
More Exercises for the Slate.
4. What is the value of any of a pound Troy? A. 10 oz. $ pwts. 167.
5. What is the value of 243 of a hogshead ? A. 49 gallony 12922 qts.
6. What is the value of 371 of a pound avoirdupois? A. 1 lb 1437 i oz.
7. What is the value of 30 of a hogshead? A. 50 gallons.
8. What is the value of 13 of a day? A. 16 hours, 36 min 56 sec.
IL, TO REDUCE FRACTIONS OF A HIGHER DENOMINA
TION INTO A LOWER. We have seen (1T XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce so £. to the fraction of a penny.
1 In this example, we multi OPERATION.
ply the 1, in ato, as in Re Numer. 1
duction of whole numbers 20 s.
viz., pounds by what makes a
pound, shillings by what 20
makes a shilling, &c. But 12 d.
this operation may be express
ed differently, thus ; 450 X New numer. 240
20 x 12= 48= d.; or, by
dividing the denominators, Then, 240
thus; 20020=24:12= =fd. Ans. Denom. 4801
. 1 d., Ans., as before, in its
A. Multiply the fraction, as in Reduction ut whole numbers.
More Exercises for the Slate. 2. Reduce zło of a pound to the fraction of a shilling.
A. The 3. Reduce 1920 of a pound to the fraction of a farthing.
A. 4. Reduce Tots of a hogshead to the fraction of a gallon.
A. To gas 5. Reduce TýT of a bushel to the fraction of a quart.
4. Iff gt 6. Reduce 1117 of a day to the fraction of a minute.
A. 1941 m. 7. Reduce Tomg of a cwt. to the fraction of a pound.
A. & I 8. Reduce bio of a hhd. to the fraction of a pint. A. pt. 9. Reduce T&o of a pound to the fraction of a shilling.
ILI. TO REDUCE FRACTIONS OF A LOT
TION INTO A EJCEER
We have seen, that, to & Tide a fract. II. *? En multiply the denominator, or CITde e EZ
This rule is the re rerse of the as, TL, 2RC PETE
duction, I IXIL, TI, PB 17
diride br in Peduction of the num
I bers. The same result in de dotzin New denom. 480 ed if performed thus: Then, tšo, Ans. Í *x 12 x2= 5 £., Års.
Hence the following
More Exercises for the Slate. 2. Reduce 1 of a shilling to the fraction of a pound.
4. zo £. 3. Reduce 1 of a farthing to the fraction of a pound.
A. 1920 £. 4. Reduce It of a gallon to the fraction of a hogshead.
A. Tobg hhd. 5. Reduce 144 of a quart to the fraction of a bushel.
A. bu. 6. Reduce 1411 of a minute to the fraction of a day.
A. TALT: 9. Reduce ☆ of a pound to the fraction of a hundred weight.
A. Toor 8. Reduce of a pint to the fraction of a hogshead.
A. 2520 =oto. 9. Reduce of a shilling to the fraction of a pound.
DECIMAL FRACTIONS. 9 LII. Q. When such fractions as these occur, viz. So, ifra 73 , how is a unit supposed to be divided ?
A. Into 10 equal parts, called tenths; and each tenth into 10 other equal parts, called hundredths, and each hundredth into 10 more equal parts, called thousandths, &c.
Q. How is it customary to write such expressions ?
A. By taking away the denominator, and placing a comma before the numerator.
Let me see you write down, in this manner, or, too, ooo
Q. What name do you give to fractions written in this manner ?
A. From the Latin word decem, signifying ten; because they increase and decrease in a tenfold proportion, like whole numbers.
Q. What are all other fractions called ?
Q. In whole numbers, we are accustomed to call the right-hand figure, units, from which we begin to reckon no cumerate; hence it was found convenient to make the swille piace a starting point in decimals, and to do this, we make use of a comma; what, then, is the use of this comma ?
A. It merely shows where the units' place is.
A. Because it separates the decimals from the whole numbers.
Q. What is the first figure at the right of the separatrix called ?